Option pricing and portfolio optimization : modern methods of financial mathematics / Ralf Korn, Elke Korn.

Format:

Book

Author/Creator:

Korn, Ralf.

Korn, Elke, 1962- author.

Series:

Graduate studies in mathematics ; v. 31.

Graduate studies in mathematics ; volume 31

Standardized Title:

Optionsbewertung und Portfolio-Optimierung. English

Language:

English

Subjects (All):

Options (Finance)--Prices--Mathematical models.

Options (Finance).

Portfolio management--Mathematical models.

Portfolio management.

Physical Description:

1 online resource (269 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2001]

Language Note:

English

Summary:

Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills. The mathematics involved in modern finance springs from the heart of probability and analysis: the Itô calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of purely mathematical topics are treated in extended "excursions" from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a self-contained and complete introduction to the underlying mathematics. This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes as applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuous-time finance that assumes familiarity with stochastic processes. The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential.

Contents:

""Exercises""""Chapter 3. Option Pricing""; ""Â 3.1. Introduction""; ""Â3.2. Option Pricing via the Replication Principle""; ""Excursion 5: Girsanov's Theorem""; ""3.2. Continuation: Option Pricing via the Replication Principle""; ""Â3.3. Option Pricing by the Partial Differential Approach""; ""Excursion 6: The Feynman-Kac Representation""; ""Â3.4. Arbitrage Bounds for American and European Options""; ""Â3.5. Pricing of American Options""; ""Â3.6. Arbitrage, Equivalent Martingale Measures and Option Pricing""; ""Â3.7. Market Numeraire and Numeraire Invariance""; ""Exercises""

""Chapter 4. Pricing of Exotic Options and Numerical Algorithms""""Â 4.1. Exotic Options with Explicit Pricing Formulae""; ""a) Path independent options on one stock""; ""b) Options on more than one underlying stock""; ""c) Path dependent options""; ""Excursion 7: Weak Convergence of Stochastic Processes""; ""Â4.2. Monte-Carlo Simulation""; ""Â 4.3. Approximation via Binomial Trees""; ""Â4.4. Trinomial Trees and Explicit Finite-Difference Methods""; ""Â4.5. The Pathwise Binomial Approach of Rogers and Stapleton""; ""Exercises""; ""Chapter 5. Optimal Portfolios""

""Â5.1. Introduction and Formulation of the Problem""""Â5.2. The Martingale Method""; ""Â5.3. Optimal Option Portfolios""; ""Excursion 8: Stochastic Control""; ""Â5.4. Portfolio Optimization via the Stochastic Control Method""; ""Exercises""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Back Cover""

Notes:

Description based upon print version of record.

Includes bibliographical references (pages 247-249) and index.

Description based on print version record.

ISBN:

1-4704-2085-6